Problem: Rewrite as a simplified fraction. ${0.59\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 593.3333...\\ 100x &= 59.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 534}$ ${x = \dfrac{534}{900}} $ ${x = \dfrac{89}{150}} $